Medical Image Analysis Image Registration Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.
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Medical Image AnalysisMedical Image AnalysisImage Registration
Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.
Image RegistrationImage Registration
Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.
Atlas◦Study the variability of anatomical
and functional structures among the subjects
Structural computerized atlas (SCA): CT or conventional MRI. ◦A model for image segmentation and
extraction of a structural volume of interest (VOI)
Image RegistrationImage Registration
Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.
Functional computerized atlas (FCA): SPECT, PET, or fMRI. ◦Understanding the metabolism of
functional activity in a specific structural VOI
Image registration methods and algorithms◦Transformation of a source image
space to the target image space
Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.
Analysis
Analysis
Anatomical Reference
(SCA)
(SCA)
Functional Reference
(FCA)
Functional Reference(FCA)
ReferenceSignatures
ReferenceSignatures
MR Image(New Subject)
MR Image(New Subject)
PET Image(New Subject)
PET Image(New Subject)
MR-PETRegistration
MR-PETRegistration
Figure 9.1. A schematic diagram of multi-modality MR-PET image analysis using computerized atlases.
Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.
AB
f
g
Figure 9.2. Image registration through transformation.
Image RegistrationImage Registration
Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.
External markers and stereotactic frames based landmark registration◦External markers◦Coordinate transformation (rotation,
translation and scaling) and interpolation computed from visible markers
◦Optimizing the mean squared error◦Stereotactic frames are usually
uncomfortable for the patient
Image RegistrationImage RegistrationRigid-body transformation based
global registration◦Principal axes transformation◦PET-PET, MR-MR, MR-PET
Image feature-based registration◦Boundary and surface matching based
registration Edges, boundary and surface information A geometric transformation is obtained by
minimizing a predefined error function between the surfaces
Image RegistrationImage Registration
Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.
◦Image landmarks and features based registration Utilize pre-defined anatomical landmarks
or features Bayesian model based probabilistic
methods Neuroanatomical atlases for elastic
matching of brain images Landmark-based elastic matching
algorithm Maximum likelihood estimation
Rigid-Body TransformationRigid-Body TransformationRigid transformation
◦ : rotation matrix◦ : translation vector
Translation along -axis by
Rt
tRxx'
x p
zz
yy
pxx
'
'
'
Rigid-Body TransformationRigid-Body TransformationTranslation along -axis by
Translation along -axis by
y q
zz
qyy
xx
'
'
'
z r
rzz
yy
xx
'
'
'
Rigid-Body TransformationRigid-Body TransformationRotation about -axis by
Rotation about -axis by
x
cossin'
sincos'
'
zyz
zyy
xx
y
cossin'
'
sincos'
zxz
yy
zxx
Rigid-Body TransformationRigid-Body TransformationRotation about -axis byz
zz
yxy
yxx
'
cossin'
sincos'
Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.
Translation of z
Translation of y Translation of x
Rotation by
Rotation by
Rotation by
Figure 9.3. The translation and rotation operations of a 3-D rigid transformation.
Rigid-Body TransformationRigid-Body Transformation
Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.
The rotation matrix for the rotational order:
R
cossin0
sincos0
001
cos0sin
010
sin0cos
100
0cossin
0sincos
RRRR
Affine TransformationAffine TransformationAffine matrix including the
translation, rotation and scaling transformation
Axx'
11000
000
000
000
1000
0cossin0
0sincos0
0001
1000
0cos0sin
0010
0sin0cos
1000
0100
00cossin
00sincos
1000
100
010
001
1
'
'
'
z
y
x
c
b
a
r
q
p
z
y
x
Principal Axes RegistrationPrincipal Axes RegistrationPrincipal axes registration (PAR)
◦ Global matching of two binary volumes
: a binary segmented volume
: centroid of
),,( zyxB
Tggg zyx ),,( ),,( zyxB
zyx
zyxg zyxB
zyxxB
x
,,
,,
),,(
),,(
Principal Axes RegistrationPrincipal Axes Registration
zyx
zyxg zyxB
zyxyB
y
,,
,,
),,(
),,(
zyx
zyxg zyxB
zyxzB
z
,,
,,
),,(
),,(
Principal Axes RegistrationPrincipal Axes RegistrationThe principal axes of
are the eigenvectors of the inertia matrix:
),,( zyxB
zzzyzx
yzyyyx
xzxyxx
III
III
III
I
zyx
ggxx zyxBzzyyI,,
22 ),,()()(
zyx
ggyy zyxBzzxxI,,
22 ),,()()(
Principal Axes RegistrationPrincipal Axes Registration
zyx
ggzz zyxByyxxI,,
22 ),,()()(
zyx
ggyxxy zyxByyxxII,,
),,())((
zyx
ggzxxz zyxBzzxxII,,
),,())((
zyx
ggzyyz zyxBzzyyII,,
),,())((
Principal Axes RegistrationPrincipal Axes RegistrationResolve 6 degrees of freedom
◦ Three rotations and three translations
Equate the normalized eigenvector matrix to the rotation matrix RRRE
333231
232221
131211
eee
eee
eee
E
Principal Axes RegistrationPrincipal Axes Registration
cossin0
sincos0
001
cos0sin
010
sin0cos
100
0cossin
0sincos
RRR
)arcsin( 31e
)cos/arcsin( 21 e
)cos/arcsin( 32 e
Principal Axes RegistrationPrincipal Axes RegistrationPAR for two volumes and
◦ 1. Translate the centroid of to the origin
◦ 2. Rotate the principal axes of to coincide with the , and axes
◦ 3. Rotate the , and axes to coincide with the principal axes of
◦ 4. Translate the origin to the centroid of
◦ is scaled to match the volume using the scaling factor
1V 2V
1V
1Vx y z
x y z
2V
2V
1V2V
3
2
1
V
VFs
Principal Axes RegistrationPrincipal Axes RegistrationProbabilistic models
◦ Counting the occurrence of a particular binary subvolume that is extracted from the registered volumes corresponding to various images
n
ii zyxS
nzyxM
1
),,(1
),,(
Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.
Figure 9.4. A 3-D model of brain ventricles obtained from registering 22 MR brain images using the PAR method.
Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.
Figure 9.5. Rotated views of the 3-D brain ventricle model shown in Figure 9.3.
Iterative Principal Axes Iterative Principal Axes RegistrationRegistrationIterative principal axes
registration (IPAR)◦ Developed by Dhawan et al.◦ Register MR and PET brain images◦ Used with partial volumes
Iteration 1
Figure 9.6. Three successive iterations of the IPAR algorithms for registration of vol 1 and vol 2: The results of the first iteration (a), the second iteration (b) and the final iteration (c). Vol 1 represents the MR data while the PET image with limited filed of view (FOV) is represented by vol 2.
(a)
Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.
Iteration 2
(b)
Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.
Iteration 3
(c)
Figures 9.7 a, b and c: Sequential slices of MR (middle rows) and PET (bottom rows) and the registered MR-PET brain images (top row) of the corresponding slices using the IPAR method.
(a)
Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.
(b)
Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.
(c)
Image Landmarks and Features Image Landmarks and Features Based RegistrationBased RegistrationImage landmarks and features Image landmarks and features
based registrationbased registration◦ Rigid and non-rigid transformationsRigid and non-rigid transformations◦ Image landmarks (points) and Image landmarks (points) and
featuresfeatures
Similarity Transformation for Similarity Transformation for Point-Based RegistrationPoint-Based RegistrationA non-rigid transformation
: ratation : scaling : translation : the total number of landmarks
)(xT
trxx s'
yxx )()( TE
sr
tN
N
iiii sw
1
22 || ytrx
Similarity Transformation for Similarity Transformation for Point-Based RegistrationPoint-Based RegistrationAlgorithm
◦ 1.◦ 2. Find
1sr
N
ii
N
iii
w
w
1
2
1
2xx
N
ii
N
iii
w
w
1
2
1
2yy
xxx ii
yyy ii
Similarity Transformation for Similarity Transformation for Point-Based RegistrationPoint-Based Registration
Singular value decomposition
◦ 3. Compute the scaling factor
◦ 4. Compute
N
i
tiiiwZ
1
2 yx
tVUZ
),,( 321 diag 0321 tdiag UVUVr ))det(,1,1(
N
iiii
N
iiii
w
ws
1
2
1
2
xxr
yxr
xryt s
Weighted Features Based Weighted Features Based RegistrationRegistration , = 1, 2, 3,…, : a set of
corresponding data shapes in and spaces
}{ iX i sN
x y
s iXN
i
N
jijijij TwTd
1 1
22 )()( yx
Elastic Deformation Based Elastic Deformation Based RegistrationRegistrationElastic deformation
◦Mimic a manual registration◦Map the elastic volume to the
reference volume◦The elastic volume is deformed by
applying external forces such that it matches the reference model
◦Constraints Smoothness incompressibility
Elastic Deformation Based Elastic Deformation Based RegistrationRegistrationMotion of a deformable body in
Lagrangian form ◦ : the force acting on a particle◦ : the position◦ : time◦ : the mass◦ : the damping constant◦ : the internal energy of
deformation
rtttf
)(
),(2
2 rrrr
),( tf rr
t
)(r
Elastic Deformation Based Elastic Deformation Based RegistrationRegistrationFind the displacement vector
that maximizes the similarity measure◦ : metric tensor◦ : curvature tensor
ijkG
ijkB
kjiijkijkijkijk dadadaBBGGS )()',(221221 xx
)',( xxS
u
MR ReferenceBrain Image
Data
Global RegistrationIPAR
Algorithm
MR NewBrain Image
Data
AnatomicalReference
Model
LandmarksLocalization and
VOICharacterization
Expert ViewerEditing andValidation
Low-ResolutionDeformation and
Matching
Spatial Relaxationand Constraint
Adapation
High-ResolutionDeformation and
Matching
Multi-Resolution DeformationBased
Local Registration andMatching
Figure 9.8. Block diagram for the MR image registration procedure.
Figure 9.9. Results of the elastic deformation based registration of 3-D MR brain images: The left column shows three images of the reference volume, the middle column shows the respective images of the brain volume to be registered and the right column shows the respective images of the registered brain volume.
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